Apparatus and method for providing a density measurement augmented for entrained gas

ABSTRACT

A flow measuring system combines a density measuring device and a device for measuring the speed of sound (SOS) propagating through the fluid flow and/or for determining the gas volume fraction (GVF) of the flow. The GVF meter measures acoustic pressures propagating through the fluids to measure the speed of sound α mix  propagating through the fluid to calculate at least gas volume fraction of the fluid and/or SOS. In response to the measured density and gas volume fraction, a processing unit determines the density of non-gaseous component of an aerated fluid flow. For three phase fluid flows, the processing unit can determine the phase fraction of the non-gaseous components of the fluid flow. The gas volume fraction (GVF) meter may include a sensing device having a plurality of strain-based or pressure sensors spaced axially along the pipe for measuring the acoustic pressures propagating through the flow.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present invention is a continuation-in-part of U.S. patentapplication Ser. No. 10/892,886 filed Jul. 15, 2004, which claimed thebenefit of U.S. Provisional Patent Application No. 60/487,832 filed Jul.15, 2003, and claims the benefit of U.S. Provisional Patent ApplicationNo. 60/548,215 filed Feb. 27, 2004, U.S. Provisional Patent ApplicationNo. 60/571,903 filed May 17, 2004, U.S. Provisional Patent ApplicationNo. 60/579,448 filed Jun. 14, 2004, U.S. Provisional Patent ApplicationNo. 60/570,321 filed May 12, 2004, U.S. Provisional Patent ApplicationNo. 60/539,640 filed Jan. 28, 2004, U.S. Provisional Patent ApplicationNo. 60/524,964 filed Nov. 25, 2003, U.S. Provisional Patent ApplicationNo. 60/512,794 filed Oct. 20, 2003, U.S. Provisional Patent ApplicationNo. 60/510,302 filed Oct. 10, 2003, U.S. Provisional Patent ApplicationNo. 60/504,785 filed Sep. 22, 2003, U.S. Provisional Patent ApplicationNo. 60/503,334 filed Sep. 16, 2003, U.S. Provisional Patent ApplicationNo. 60/491,860 filed Aug. 1, 2003, which are all incorporated herein byreference.

TECHNICAL FIELD

This invention relates to an apparatus for measuring the density of afluid flow having entrained gas therein, and more particularly to anapparatus that measures the speed of sound propagating through the flowto determine the gas volume fraction of the flow in the process toaugment or correct the density measurement of a density meter and/or toprovide a composition measurement compensated for entrained gas.

BACKGROUND ART

Density meters are commonly used instruments in industrial processes.Common types of density meters include nuclear densitometers, vibratingvane densitometers and Coriolis flow meters having a density measurementas a by-product measurement.

In most applications, density measurements are used to discern bulkproperties of the process fluid. Typically, density measurements areintended to provide information about the liquid and solid phases of aprocess fluid. These measurements get confound when an unknown amount ofentrained air is present.

For a two-component mixture, knowing the component densities andaccurately measuring the mixture density provides a means to determinethe phase fractions of each of the two components. However, the presenceof a third phase, such as entrained air (or gas) confounds thisrelationship. Typically, there is not significant contrast in thedensities of the liquid components, which results in large errors inphase fraction determination resulting from small levels of entrainedair.

The measurement of slurries used in the paper and pulp industries and inother industries particularly presents problems in the production ofpaper. Slurries commonly used in the paper and pulp industry are mostlywater and typically contain between 1% and 10% pulp content by mass.Monitoring the gas volume fraction of a slurry can lead to improvedquality and efficiency of the paper production process.

Processes run in the paper and pulp industry can often, eitherintentionally or unintentionally, entrain gas/air. Typically, thisentrained air results in measurement errors in process monitoringequipment such as density meters. Industry estimates indicate thatentrained air levels of 2–4% are common. Since most density meters areunable to distinguish between air and liquid, interpreting their outputas a density measurement or composition measurement would result in anoverestimate of the density of the liquid or slurry present at themeasurement location. Similarly, the void fraction of the air within thepipe can cause errors in compositional measurements.

Thus, providing a method and apparatus for measuring entrained air inpaper and pulp slurries, for example, would provide an accuratemeasurement of the entrained air and would provide a means to correctthe output of density meters.

As suggested, multiphase process flow rate is a critical process controlparameter for the paper and pulp industry. Knowing the amounts ofliquid, solids and entrained gases flowing in process lines is key tooptimizing the overall the papermaking process. Unfortunately,significant challenges remain in the achieving accurate, reliable, andeconomical monitoring of multiphase flow rates of paper and pulpslurries. Reliability challenges arise due the corrosive and erosiveproperties of the slurry. Accuracy challenges stem from the multiphasenature of the slurries. Economical challenges arise from the need toreduce total lifetime cost of flow measurement, considering installationand maintenance costs in addition to the initial cost of the equipment.

Currently, there is an unmet need for multiphase flow measurement in theprocessing industry, such as the paper and pulp industry. Real time flowmeasurement is typically restricted to monitoring the total volumetricflow rate in a process line without providing information on thecomposition of the process mixture.

Similarly, well head monitoring represents a difficult technicalchallenge with the presence of entrained gas. Metering well headproduction rates is a long standing challenge for the oil and gasindustry. Performing accurate and timely monitoring of the productionrates has many benefits, which include optimizing overall field andspecific well production. The difficulty is due in no small part to theextreme variability of produced fluids which can include various typesand mixtures of oil, water, gas, and solid particles.

Many companies have developed various types of three phase metersdesigned to address the well head flow metering market. These productshave met relatively limited commercial success due to a combination ofperformance, accuracy, and cost issues. This disclosure provide an meansand apparatus for well head monitoring that combines multiple existingtechnologies in to system that should meet a wide range of cost andperformance goals.

It is proposed herein to use sonar-based entrained gas measurement todetermine the entrained gas level in conjunction with any mixturedensity measurement to improve the accuracy and therefore value of thedensity measurement. A sound speed based entrained gas measurement canaccurately determine the entrained gas in an aerated mixture withoutprecise knowledge of the composition of either the non-gas components ofthe multiphase mixture of the composition of gas itself. Thus, theentrained gas levels can be determined essentially independent of thedetermination of the liquid properties. The accuracy could be improvedusing the sound speed measurement and mixture density simultaneously,but is not required. Determining the entrained gas level enables thedensity measurement to determine the properties of non-gas component ofthe multiphase mixture with the same precision as if the gas was notpresent. This capability also enables the density meters to providesignificantly enhanced compositional information for aerated mixtures.

SUMMARY OF THE INVENTION

Objects of the present invention include an apparatus having a devicefor determining the speed of sound propagating within a fluid flow in apipe to determine the gas volume fraction of a process fluid or flowflowing within a pipe, and augment to improve the accuracy of a densitymeasurement of a density meter and/or to provide a compositionmeasurement compensated for entrained gas.

According to the present invention, a flow measuring system fordetermining the density of a fluid flowing in a pipe is provided. Themeasuring system comprises a density meter that provides a densitysignal indicative of the density of the fluid flowing in the pipe. Aflow measuring device measures the speed of sound propagating throughthe fluid. The measuring device provides an SOS signal indicative of thespeed of sound propagating through the fluid and/or a GVF signalindicative of the gas volume fraction of the fluid. A processing unitdetermines the density of the non-gaseous component of the aerated fluidin response to the SOS signal and/or the GVF signal and the densitysignal.

According to the present invention, a well head metering system formeasuring density of non-gaseous components of a three phase fluidflowing in a pipe is provided. The metering system comprises a densitymeter that provides a density signal indicative of the density of thefluid flowing in the pipe. A flow measuring device measures the speed ofsound propagating through the fluid. The measuring device provides anSOS signal indicative of the speed of sound propagating through thefluid and/or a GVF signal indicative of the gas volume fraction of thefluid. A processing unit determines the density of the non-gaseouscomponent of the aerated fluid in response to the SOS signal and/or theGVF signal and the density signal.

The foregoing and other objects, features and advantages of the presentinvention will become more apparent in light of the following detaileddescription of exemplary embodiments thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a flow measuring system forproviding a density and/or composition measurement augmented forentrained gas within an aerated fluid flow passing within a pipe, inaccordance with the present invention.

FIG. 2 is a schematic illustration of another flow measuring system forproviding a density and/or composition measurement augmented forentrained gas within an aerated fluid flow passing within a pipe, inaccordance with the present invention.

FIG. 3 is a function block diagram of a processing unit of flowmeasuring system similar to that of FIG. 1, in accordance with thepresent invention.

FIG. 4 is a schematic illustration of a flow measuring system forproviding a density and/or composition measurement provided by a gammadensitometer augmented for entrained gas within a bitumen froth flowpassing within a pipe, in accordance with the present invention.

FIG. 5 is a plot of the relative error in the interpreted percent solidsversus the gas volume fraction in a bitumen froth flow, in accordancewith the present invention.

FIG. 6 is a schematic illustration of a flow measuring system forproviding a density and/or composition measurement provided by acoriolis meter augmented for entrained gas within a bitumen froth flowpassing within a pipe, in accordance with the present invention.

FIG. 7 is a function block diagram of a processing unit of flowmeasuring system similar to that of FIG. 6, in accordance with thepresent invention.

FIG. 8 is a schematic illustration of model of a coriolis meter havingaerated fluid flowing therethrough that accounts for compressibility andinhomogeniety of the aerated fluid, in accordance with the presentinvention.

FIG. 9 is a schematic illustration of a well head monitoring system forproviding a density and/or composition measurement provided by acoriolis meter augmented for entrained gas within a bitumen froth flowpassing within a pipe, in accordance with the present invention.

FIG. 10 is a plot of three phase composition of an aerated hydrocarbonand water fluid flow as a function of sound speed and flow density, inaccordance with the present invention.

FIG. 11 is another embodiment of a function block diagram of aprocessing unit of flow measuring system similar to that of FIG. 7, inaccordance with the present invention.

FIG. 12 is a plot the density correction and gas volume fraction of afluid determined by a flow system embodying the present invention

FIG. 13 is a plot of net oil error and watercut of three phase fluidflow determined by a flow system embodying the present invention.

FIG. 14 is a plot of a snap shot of three phase fluid flow determined bya flow system embodying the present invention.

FIG. 15 is a schematic block diagram of a gas volume fraction meter, inaccordance with the present invention.

FIG. 16 is a schematic block diagram of another embodiment of gas volumefraction meter, in accordance with the present invention.

FIG. 17 is a kω plot of data processed from an array of pressure sensorsuse to measure the speed of sound of a fluid flow passing in a pipe, inaccordance with the present invention.

FIG. 18 is a plot of the speed of sound of the fluid flow as a functionof the gas volume fraction over a range of different pressures, inaccordance with the present invention.

FIG. 19 is a schematic block diagram of a volumetric flow meter havingan array of sensor, in accordance with the present invention.

FIG. 20 is a graphical cross-sectional view of the fluid flowpropagating through a pipe, in accordance with the present invention.

FIG. 21 is a kω plot of data processed from an array of pressure sensorsuse to measure the velocity of a fluid flow passing in a pipe, inaccordance with the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Density meters 16 provide a measurement of the density of a fluid flow12 passing through a pipe 14. As described in detail hereinbefore, adensity meter provides erroneous density measurements in the presence ofentrained gas (e.g., bubbly gas) within the fluid flow. The presentinvention provides a means for augmenting or compensating the densitymeter to determine improved density measurements that provides thedensity of the non-gas portion of the fluid flow 12. The density metermay be any device capable of measuring the density of the fluid flow,such as nuclear densitometers, vibrating vane densitometers and Coriolisflow meters, which provide a density measurement as a by-productmeasurement.

The present invention proposes the use of sonar-based entrained gasmeasurements to determine the entrained gas level in conjunction withany density measurement of a mixture flowing in a pipe to improve theaccuracy, and therefore value of the density measurement. A sound speedbased entrained gas measurement can accurately determine the entrainedgas in an aerated mixture without precise knowledge of the compositionof either the non-gas components of the multiphase mixture or thecomposition of gas itself. Thus, the entrained gas levels can bedetermined essentially independent of the determination of the liquidproperties. The accuracy could be improved using the sound speedmeasurement and mixture density simultaneously, but is not required.Determining the entrained gas level enables the density measurement todetermine the properties of non-gas component of the multiphase mixturewith the same precision as if the gas was not present. This capabilityalso enables the density meters to provide significantly enhancedcompositional information for aerated mixtures.

As shown in FIG. 1, one embodiment of a flow measuring system 10embodying the present invention includes a density meter 16, a speed ofsound (SOS) measuring apparatus 18 and a processing unit 20 to provideany one or more of the following parameters of the fluid flow 12,namely, gas volume fraction, speed of sound propagating through thefluid flow, uncompensated density, compensated density and composition.The fluid flow may be any aerated fluid or mixture including liquid,slurries, solid/liquid mixture, liquid/liquid mixture, solid/solidmixture and any other multiphase flow having entrained gas.

In this embodiment, the density meter 16 provides a signal 22 indicativeof the density of the fluid flow 12 not augmented or compensated forentrained gas. The SOS measuring apparatus 18 provides an SOS signal 24indicative of the speed of sound propagating through the fluid flow. Aprocessing unit 20 determines at least one of the parameters of thefluid flow described hereinbefore in response to the SOS signal 24 anddensity signal 22. Pressure and/or temperature signals 26,28 may also beprovided to the processing unit 20, which may be used to provide moreaccurate measurements of the gas volume fraction. The pressure andtemperature may be measured by known means or estimated.

The SOS measuring device 18 includes any means for measuring the speedof sound propagating through the aerated flow 12. One method includes apair of ultra-sonic sensors axially spaced along the pipe 14, whereinthe time of flight of an ultrasonic signal propagating between anultra-sonic transmitter and receiver is indicative of the speed ofsound. Depending on the characteristics of the flow, the frequency ofthe ultra-sonic signal must be relating low to reduce scatter within theflow. The meter is similar as that described in U.S. patent applicationSer. No. 10/756,922 filed on Jan. 13, 2004, which is incorporated hereinby reference.

Alternatively, a flow measuring system 30 embodying the presentinvention, as shown in FIGS. 2, 7 and 11, provides a gas volume fraction(GVF) meter 100 for determining the gas volume fraction of the fluidflow 12, which will be described in greater detail hereinafter. The GVFmeter 100 comprises a sensing device 116 having a plurality ofstrain-based or pressure sensors 118–121 spaced axially along the pipefor measuring the acoustic pressures 190 propagating through the flow12. The GVF meter determines and provides a first signal 27 indicativeof the SOS propagating through the fluid flow 12 and a second signal 29indicative of the gas volume fraction (GVF) of the flow 12, which willbe described in greater detail hereinafter. The gas volume fractionmeter 100 is similar to that described in U.S. patent application Ser.No. 10/762,410 filed on Jan. 21, 2004, which is incorporated herein byreference. The processing unit 32 determines at least one of theparameters of the fluid flow described hereinbefore in response to theSOS signal 24 and/or GVF signal 29, and the density signal 22.

FIG. 3 illustrates a functional block diagram 40 of the flow measuringsystem 30 of FIG. 2. As shown, the GVF meter 100 measures acousticpressures propagating through the fluids 12, thereby measuring the speedof sound α_(mix) propagating through the fluid flow 12 at 42. The GVFmeter 100 calculates the gas volume fraction of the fluid using themeasured speed of sound at 44. The GVF meter may also use the pressureof the process flow to determine the gas volume fraction. The pressuremay be measured or estimated at 46.

For determining an improved density 48 (i.e., density of non-gas portionof flow 12), the calculated gas volume fraction 29 is provided to theprocessing unit 32. Knowing the gas volume fraction 29 (and/or speed ofsound 27 propagating through the flow) and the measured density 22, theprocessing unit 32 can determine density of the non-gas portion of themultiphase flow 12.

Specifically, the density (ρ_(mix)) 22 of an aerated flow 12 is relatedto the volumetric phase fraction of the components (ø_(i)) and thedensity of the components (ρ_(i)).

$\rho_{mix} = {\sum\limits_{i = 1}^{N}{\phi_{i}\rho_{i}}}$

Where continuity requires:

${\sum\limits_{i = 1}^{N}\phi_{i}} = 1$

For example, for a two-component fluid flow:ρ_(mix)=ρ_(nongas)φ_(nongas)+ρ_(gas)φ_(gas)therefore,ρ_(nongas)=(ρ_(mix)−ρ_(gas)φ_(gas))/φ_(nongas)=(ρ_(mix)−ρ_(gas)φ_(gas))/1−φ_(gas),wherein φ_(nongas)=1−φ_(gas)

Assuming the density of the gas (ρ_(gas)) is substantially less than thedensity of the non-gas portion (ρ_(nongas)) of the fluid flow 12, theequation can be reduced to:ρ_(nongas)=ρ_(mix)/(1−φ_(gas))wherein ρ_(mix) is the density of the mixture, ρ_(nongas), ø_(nongas)are the density and phase fraction, respectively, of a non-gas componentof the fluid flow, and ρ_(gas), ø_(gas) are the density and phasefraction, respectively, of the entrained gas within the mixture.

Therefore, knowing the density (ρ_(gas)) of the gas/air, the measuredgas volume fraction of the gas (ø_(gas)), and the improved densitymeasurement (ρ_(mix)) of the aerated flow to be compensated forentrained gas enable the density (ρ_(nongas)) of the non-gas portion ofthe aerated flow 12 to be determined, which provides improvedcompositional information of the aerated flow 12. For instances when thedensity of the gas component is substantially greater than the non-gascomponent, knowing just the measured density (ρ_(mix)) 22 of the aeratedflow 12 density of the gas component and the gas volume fraction(ø_(gas)) 29 is sufficient to determine the density (ρ_(nongas)) 48 ofthe non-gas component of the flow 12.

The present invention further contemplates determining improvedcompositional information of the aerated flow 12.

When a two-component mixture 12 includes a third component of entrainedgas or gas, the relationship is as follows:ρ_(mix)=ρ₁φ₁+ρ₂φ₂+ρ_(gas)φ_(gas)therefore, φ₁=[ρ_(mix)−ρ_(gas)φ_(gas)−ρ₂(1−φ_(gas))]/(ρ₁−ρ₂), whereφ₂=1−φ₁−φ_(gas)

assuming the density of the gas (ρ_(gas)) is substantially less than thedensity of the non-gas portion (ρ_(nongas)) of the fluid flow 12, theequation can be reduced to:φ₁=[ρ_(mix)−ρ₂(1−φ_(gas))]/(ρ₁−ρ₂)

Therefore, knowing the density (ρ_(gas)) of the gas/air and the measureddensity of the gas volume fraction (ø_(gas)) enables density measurement(ρ_(mix)) of the mixture to be compensated for entrained gas and providea density measurement of only the two-component mixture that does notinclude the density of the entrained air/gas at 50.

Furthermore, knowing the densities of each of the components of themixture (ρ₁, ρ₂) and the density of the gas/air (ρ_(gas)), and knowingthe measured densities of the mixture (ρ_(mix)) and gas volume fraction(ø_(gas)) enable the volume fraction of each component (ø₁, ø₂) to bedetermined at 52.

Referring to FIG. 4, one example of an application for the flowmeasuring system 30 is in the oil sands industry, where monitoringentrained sand levels in bitumen/water froths is an importantapplication. However, due to the presence of unknown amount of entrainedair in the froth, an accurate measurement of the amount of particles(e.g., sand) is not possible using a gamma densitometer 60 operating ona bitumen froth mixture 12, which contains a small amount of entrainedair and sand particles entrained in a liquid continuous mixture ofbitumen and water. The density of bitumen and water (ρ₁) are nearlyidentical for most applications, therefore, variations in thebitumen/water cut of liquid phase has very limited effect on the mixturedensity. Variations in the mixture density are therefore due to the airand particles. The density of the particles (ρ₂) and the density of theair (ρ_(gas)) are known. By measuring the gas volume fraction of theentrained air (ø_(gas)) and density of the fluid flow (ρ_(mix)) directlyand knowing the density of the particles (ρ₂) and the density of thebitumen and water (ρ₁), the gamma densitometer 60 in combination withthe entrained gas meter 100 provides a means to determine the amount ofsand left (ø₂) in the slurry as well as other parameters of the mixture,as described hereinbefore.

FIG. 5 is a plot of the relative error in interpreted percent of solidsin a bitumen froth flow versus the gas fraction of entrained air/gas inthe flow 12. As shown, a bitumen froth flow having 1% of entrained airtherein results in an approximately 20% error in percent solids (e.g.,sand) in the bitumen froth flow.

As shown in FIG. 4, the density measurement (ρ_(nongas)) and compositionmeasurement (ø₁, ø₂) described above can be done on the full pipe, or asshown in FIG. 6, on a slip stream pipe 70. Referring to FIG. 6, a slipstream pipe 70 enables the use of a coriolis meter 72 to measure thedensity (ρ_(mix)) by providing a smaller diameter pipe. A furtherbenefit of a sonar-based entrained air measurement is achieved when thesound speed measurement is used to enhance the accuracy of the coriolison the aerated mixture, similar to that described in U.S. patentapplication Ser. No. 10/892,886, filed on Jul. 15, 2004, which isincorporated herein by reference. While the entrained gas meter 100 isshown mounted on the full pipe in FIG. 6, the present inventioncontemplates that the entrained air meter may be mounted on the slipstream pipe 70.

As shown in FIGS. 4 and 6, the apparatus 100 for measuring the gasvolume fraction of the flow 12 may also provide a velocity measurementand a volumetric flow rate measurement of the flow, similar to thatdescribed in U.S. patent application Ser. No. 10/712,818, filed on Nov.12, 2003, U.S. patent application Ser. No. 10/712,833, filed on Nov. 12,2003, U.S. patent application Ser. No. 10/766,440, filed on Jan. 27,2004, and U.S. patent application Ser. No. 10/875,857, filed on Jun. 24,2004, which are incorporated herein by reference.

Coriolis meters provide a measurement of the mass flow and/or density ofa fluid flow 12 passing through a pipe 14. A coriolis meter provideserroneous mass flow and density measurements in the presence ofentrained gas within the fluid flow (e.g., bubbly gas). The presentinvention may also provide a means for compensating the coriolis meterto provide corrected or improved density and/or mass flow measurements.

While the gas volume fraction meter 100 may be used to determine thedensity of the non-gas component of the flow 12 and the composition of amulti-phase flow 12 as described hereinbefore, the GVF meter may be alsoused to compensate or augment the output density measurement and themass flow measurement of a coriolis meter, similar to that described inU.S. patent application Ser. No. 10/892,886 filed Jul. 15, 2004, whichis incorporated herein by reference.

In this embodiment, the coriolis meter 16 provides a frequency signal(f_(nat)) indicative of the natural frequency of the fluid 12 loadedtubes of the coriolis meter and the phase signal (Δφ) indicative of thephase lag in the tubes of the coriolis meter. The GVF meter 100 or SOSmeasuring apparatus 18 provides an SOS signal 24 indicative of the speedof sound propagating through the fluid flow. A processing unit 32processes the frequency signal, the phase signal and the SOS signal toprovide at least one of the parameters of the fluid flow describedhereinbefore, including the mass flow of the flow 12. Pressure and/ortemperature signals may also be provided to the processing unit 32,which may be used to provide more accurate measurements of the gasvolume fraction. The pressure and temperature may be measured by knownmeans or estimated.

The coriolis meter may be any known coriolis meter, such as two inchbent tube coriolis meter manufactured my MicroMotion Inc. and a two instraight tube coriolic meter manufactured by Endress & Hauser Inc. Thecoriolis meters comprise a pair of bent tubes (e.g. U-shaped, pretzelshaped) or straight tubes as will be described hereinafter.

FIG. 7 illustrates a functional block diagram 80 of the flow measuringsystem of FIG. 2. As shown, the GVF meter 100 measures acousticpressures propagating through the fluids to measure the speed of soundα_(mix). The GVF meter calculates at least gas volume fraction of thefluid and/or the reduced natural frequency using the measured speed ofsound. The GVF meter may also use the pressure of the process flow todetermine the gas volume fraction.

For determining an improved density for the coriolis meter, thecalculated gas volume fraction and/or reduced frequency is provided tothe processing unit 21. The improved density is determined usinganalytically derived or empirically derived density calibration models(or formulas derived therefore), which is a function of the measurednatural frequency and at least one of the determined GVF, reducedfrequency and speed of sound, or any combination thereof, which will bedescribed in greater detail hereinafter. The improved densitymeasurement is the density of the aerated flow passing through the pipe.

The present invention further contemplates determining improvedcompositional information of the aerated flow. In other words, knowingthe speed of sound propagating through the flow and the improveddensity, the processing unit 21 can determine phase fraction of eachcomponent of the multiphase flow.

The present invention also contemplates compensating or improving themass flow rate measurement of the coriolis meter 16, as shown in FIG. 7.For determining an improved mass flow rate for the coriolis meter, thecalculated gas volume fraction and/or reduced frequency is provided tothe processing unit 32. The improved mass flow rate is determined usinganalytically derived or empirically derived mass flow calibration models(or formulas derived therefore), which is a function of the measuredphase difference (Δφ) and at least one of the determined GVF, reducedfrequency and speed of sound, or any combination thereof, which will bedescribed in greater detail hereinafter. For determining an improveddensity for the coriolis meter, the calculated gas volume fractionand/or reduced frequency is provided to the processing unit 32. Theimproved density is determined using analytically derived or empiricallyderived density calibration/parameter models (or formulas derivedtherefore), which is a function of the measured natural frequency and atleast one of the determined GVF, reduced frequency and speed of sound,or any combination thereof, which will be described in greater detailhereinafter. The improved mass flow measurement is the mass flow rate ofthe aerated flow passing through the pipe.

While the improved mass flow and improved density measurement may be afunction GVF, SOS and reduced frequency, the present inventioncontemplates these improved measurements may be a function of otherparameters, such a gas damping ζ_(gas).

Further, while the functional block diagram illustrates that theprocessing unit 32 may improve both the density measurement and thedensity measurement of the coriolis meter 16, the invention contemplatesthat the processing may only compensate or improve one the density andmass flow rate parameters.

Results for a lumped parameter model of FIG. 8 presented hereinafterconfirm long recognized accuracy degradation of vibrating tube densitymeters attributed to aeration. The models can be used to illustratequalitatively the role of several non-dimensional parameters that governthe performance of the meters in aerated fluids. It can be concludedfrom these models that gas volume fraction plays a dominant role, withseveral other parameters including gas damping ζ_(gas) and reducedfrequency also influencing performance.

The present invention provides an approach in which a speed-of-soundmeasurement of the process fluid is integrated with the naturalfrequency measurement of a vibrating tube density meter to form a systemwith an enhanced ability to operate accurately in aerated fluids.Introducing a real time, speed-of-sound measurement address the effectsof aeration on multiple levels with the intent to enablevibrating-tube-based density measurement to continue to report liquiddensity in the presence of entrained air with accuracy approaching thatfor a non-aerated liquid. Firstly, by measuring the process sound speedwith process pressure, the aeration level of the process fluid can bedetermined with high accuracy on a real time basis. Secondly, the realtime measurements of sound speed, and the derived measurement of gasvolume fraction, are then utilized with empirically derived correctionfactors to improve the interpretation of the measured natural frequencyof the vibrating tubes in terms of the density of the aerated fluid.Thirdly, the combined knowledge of aerated mixture density and aeratedmixture sound speed, enable the determination of the non-aerated liquidcomponent density, providing improved compositional information. Noteliquids phase includes pure liquids, mixtures of liquids, as well asliquid/solid mixtures.

To illustrate the fundamental ways in which aeration impactsvibrating-tube density measurements, a simplified, lumped parametermodel for the effects of aeration in vibrating tubes is developed. Themodel illustrates that the effects of aeration can be attributed to atleast two independent mechanisms; 1) the density inhomogeniety ofdiscrete gas bubbles and 2) increased mixture compressibility due toaeration.

This basic framework provides an accurate means to determine processfluid density under most operating conditions. However, some of thefundamental assumptions regarding the interaction of the fluid 12 andthe structure can deteriorate under different operating conditions.Specifically, aerated fluids in oscillating tubes behave differentlyfrom single phase fluids in two important ways; increasedcompressibility, and fluid inhomogeneity.

Fluid Compressibility

It is well known that most aerated liquids are significantly morecompressible than non-aerated liquids. Compressibility of a fluid isdirectly related to the speed of sound and density of the fluid 12.

Mixture density and sound speed can be related to component densitiesand sound speed through the following mixing rules which are applicableto single phase and well-dispersed mixtures and form the basis forspeed-of-sound-based entrained air measurement.

$\kappa_{mix} = {\frac{1}{\rho_{mix}a_{{mix}_{\infty}}^{2}} = {\sum\limits_{i = 1}^{N}\frac{\phi_{i}}{\rho_{i}a_{i}^{2}}}}$

where

$\rho_{mix} = {\sum\limits_{i = 1}^{N}{\rho_{i}\phi_{i}}}$and κ_(mix) is the mixture compressibility, and φ_(i) is the componentvolumetric phase fraction.

Consistent with the above relations, introducing air into waterdramatically increases the compressibility of the mixture 12. Forinstance, at ambient pressure, air is approximately 25,000 times morecompressible than water. Thus, adding 1% entrained air increases thecompressibility of the mixture by a factor of 250. Conceptually, thisincrease in compressibility introduces dynamic effects that cause thedynamic of behavior of the aerated mixture within the oscillating tubeto differ from that of the essentially incompressible single-phasefluid.

The effect of compressibility of the fluid 12 can be incorporated into alumped parameter model of a vibrating tube as shown schematically inFIG. 8. The stiffness of the spring represents the compressibility ofthe fluid. As the compressibility approaches zero, the spring stiffnessapproaches infinity.

As before the effective mass of the fluid 12 is proportional to thedensity of the fluid and the geometry of the flow tube. The naturalfrequency of the first transverse acoustic mode in a circular duct canbe used to estimate an appropriate spring constant for the model

$f = {{\frac{1.84}{\pi\; D}a_{mix}} = {\frac{1}{2\;\pi}\sqrt{\frac{K_{fluid}}{m_{fluid}}}}}$

Note that this frequency corresponds to a wavelength of an acousticoscillation of approximately two diameters, i.e., this transverse modeis closely related to a “half wavelength” acoustic resonance of thetube. For low levels of entrained air, the frequency of the firsttransverse acoustic mode is quite high compared to the typicalstructural resonant frequencies of coriolis meters of 100 Hz, however,the resonant acoustic frequency decreases rapidly with increased levelsof entrained air.

In characterizing aeroelastic systems, it is often convenient to definea reduced frequency parameter to gauge the significance of theinteraction between coupled dynamic systems. For a vibrating tube filledwith fluid, a reduced frequency can be defined as a ratio of the naturalfrequency of the structural system to that of the fluid dynamic system.

$f_{red} = \frac{f_{struct}D}{a_{mix}}$

Where f_(struct) is the natural frequency of the tubes in vacuum, D isthe diameter of the tubes, and a_(mix) is the sound speed of the processfluid. For this application, as the reduced frequency becomes negligiblecompared to 1, the system approaches quasi-steady operation. In thesecases, models, which neglect the compressibility of the fluid is likelyto be suitable. However, the effects of unsteadiness increase withincreasing reduced frequency. For a given coriolis meter, mixture soundspeed has the dominant influence of changes in reduced frequency. Whenconsidering coriolis meters of varying design parameters, increases intube natural frequency or tube diameter will increase the effects ofunsteadiness for a given level of aeration.

Fluid Inhomogeneity

In additional to dramatically increasing the compressibility of thefluid 12, aeration introduces inhomogeneity to the fluid. For flowregimes in which the gas is entrained in a liquid-continuous flow field,the first-order effects of the aeration can be modeled using bubbletheory. By considering the motion of an incompressible sphere of densityof ρ₀ contained in an inviscid, incompressible fluid with a density of ρand set into motion by the fluid show that the velocity of the sphere isgiven by:

$V_{sphere} = {\frac{3\;\rho}{\rho + {2\;\rho_{0}}}V_{fluid}}$

For most entrained gases in liquids, the density of the sphere is ordersof magnitude below that of the liquid and the velocity of bubbleapproaches three times that of the fluid.

Considering this result in the context of the motion of a sphere in across section of a vibrating tube, the increased motion of the spherecompared to the remaining fluid must result in a portion of theremaining fluid having a reduced level of participation in oscillation,resulting in a reduced, apparent system inertia.

In a lumped parameter model, a gas bubble of volume fraction φ isconnected across a fulcrum 42 to a compensating mass of fluid withvolume 2Γ, where Γ is the gas volume fraction of the flow. The fulcrumis rigidly connected to the outer pipe 14. The effects of viscosity canbe modeled using a damper connected to restrict the motion of the gasbubble with respect to the rest of the liquid and the tube itself. Theremaining volume of liquid in the tube cross section (1–3Γ) is filledwith an inviscid fluid. In the inviscid limit, the compensating mass offluid (2Γ) does not participate in the oscillations, and the velocity ofthe mass-less gas bubble becomes three times the velocity of the tube.The effect of this relative motion is to reduce the effective inertia ofthe fluid inside the tube to (1–3Γtimes that presented by a homogeneousfluid-filled the tube. In the limit of high viscosity, the increaseddamping constant minimizes the relative motion between the gas bubbleand the liquid, and the effective inertia of the aerated fluidapproaches 1-Γ. The effective inertia predicted by this model of anaerated, but incompressible, fluid oscillating within a tube agrees withthose presented by (Hemp, et al, 2003) in the limits of high and lowviscosities.

One should appreciate that the processing unit may use these modelsindependently or together in a lumped parameter model.

Combined Lumped Parameter Model

Models were presented with the effects of aeration on vibrating tubedensity meters in which the effects of compressibility and inhomogenietywere addressed independently. FIG. 8 shows a schematic of a lumpedparameter model that incorporates the effects of compressibility andinhomogeniety using the mechanism-specific models developed above.

The equations of motion of the above lumped parameter model, assumingsolutions in the form of e^(st) where s is the complex frequency, can beexpressed in non-dimensional form as:

${\begin{bmatrix}{s + {2\;\alpha\;\zeta_{f}Q} + {2\;\zeta_{s}}} & {1 + {\alpha\; Q^{2}}} & {{- 2}\;\alpha\;\zeta_{f}Q} & {{- \alpha}\; Q^{2}} & 0 & 0 \\{- 1} & s & 0 & 0 & 0 & 0 \\{2\;\zeta_{f}Q} & {- Q^{2}} & {{\left( {1 - {3\;\Gamma}} \right)s} + {2\;\zeta_{f}Q} + {2\;\zeta_{g}}} & Q^{2} & {{- 2}\;\zeta_{g}} & 0 \\0 & 0 & {- 1} & s & 0 & 0 \\0 & 0 & {{- 2}\;\zeta_{g}} & 0 & {{2\;\Gamma\; s} + {2\;\zeta_{g}}} & 0 \\0 & 0 & 0 & 0 & {- 1} & s\end{bmatrix}\begin{Bmatrix}y_{1} \\x_{1} \\y_{2} \\x_{2} \\y_{3} \\x_{3}\end{Bmatrix}} = 0$

The parameters governing the dynamic response of the model are definedin the following Table 1.

TABLE 1 Definition of Non-dimensional Parameters Governing the Equationof Motion for the Lumped Parameter Model of a Tube Filled with aCompressible, Aerated Fluid Symbol Description Definition α Mass ratiom_(fluid)/m_(struct) Q Natural Frequency Ratio ω_(fluid)/ω_(struct)ζ_(f) Critical Damping Ratio of Fluid Systemb_(fluid)/(2m_(fluid)ω_(fluid)) ζ_(s) Critical Damping Ratio ofStructural b_(struc)/(2m_(struct)ω_(sstruc)) System ζ_(g) CriticalDamping Ratio of Structural b_(gas)/(2m_(fluid)ω_(struct)) System τNon-dimensional time t ω_(struct) y Non-dimensional temporal derivativeof x dx/dτ

Solving the sixth-order eigenvalue problem described above provides ameans to assess the influence of the various parameters on the observeddensity. The natural frequency of the primary tube mode predicted by theeigenvalue analysis is input into the frequency/density from thequasi-steady, homogeneous model to determine the apparent density of thefluid 12 as follows.

$\rho_{apparent} = {\frac{\rho_{liq}}{\alpha}\left( {\frac{f_{s}^{2}}{f_{observed}^{2}} - 1} \right)}$

As a baseline condition, a “representative” coriolis meter withparameters given in Table 2 was analyzed.

TABLE 2 Parameters Defining tbe Baseline Vibrating Tube Density MeterParameter Description Value f_(s) Structural Frequency of Tubes 100 Hz αMass ratio 1.25 ζ_(struct) Critical Damping Ratio - 0.01 structureζ_(fluid) Critical Damping Ratio - fluid 0.01 ζ_(gas) Critical DampingRatio - gas 0.01 Q Frequency Ratio As determined by sound speed ofair/water at STP and structural parameters D Tube diameter 1.0 inches

For a given coriolis meter, the level of aeration has a dominant effecton the difference between actual and apparent mixture density. However,other parameters identified by the lumped parameter model also playimportant roles. For example, the damping parameter associated with themovement of the gas bubble relative to the fluid within the tube,ζ_(gas), is a parameter governing the response of the system toaeration. For ζ_(gas) approaching zero, the apparent density approaches1–3Γ, i.e., the meter under reports the density of the aerated mixtureby 2Γ. However, as the ζ_(gas) is increased, the apparent densityapproaches the actual fluid density of 1-Γ.

The influence of compressibility is function of gas volume fraction fora range of meters differing only in natural frequency of the tubes. Thenatural frequency of the tubes, primarily through the influence of thereduced frequency of operation at a given level of aeration cansignificantly influence the relation between the actual and apparentdensity of an aerated fluid.

Mass Flow Correction

The current state-of-the-art appears to utilize quasi-steady models, andempirical correlations based on quasi-steady models, to relate themeasured quantities to the derived fluid parameters. This quasi-steadymodel for the fluid structure interactions appears to work adequatelyfor most Coriolis meters operating with most industrial process flows.The validity of the quasi-steady assumption will scale with the reducedfrequencies of the vibration of the fluid within the pipe. Under aquasi-steady framework, the higher the reduced frequencies, the lessaccurate the Coriolis meters become.

One relevant reduced frequency for the unsteady effects within aCorilois meter is the reduced frequency based on the vibrationalfrequency, tube diameter, and process fluid sound speed:

${\overset{\sim}{f}}_{D} = \frac{fD}{a_{mix}}$

Another relevant reduced frequency is the that based on the overalllength of the corilois tubes:

${\overset{\sim}{f}}_{L} = \frac{fL}{a_{mix}}$

It should be noted that, for any given meter design in which thegeometry is fixed, the two reduced frequencies are not independent, andare scalar multiples of each other. For a given meter, variations in thereduced frequencies above are primarily determined by variations inprocess fluid sound speed.

Physically, the reduced frequency represents the ratio between the timerequired for sound to propagate over a characteristic length to the timerequired for the tube to vibrate one cycle. From a performance andaccuracy perspective, reduced frequencies serve to capture theimportance of unsteadiness in the aeroelastic interaction of the fluidand structure.

In the limit of reduced frequencies approaching zero, the process can bemodelled as quasi-steady. Most analytical models of Corilois flow metersuse a quasi-steady model for the fluid/structure interaction. However,for non-zero reduced frequencies, unsteady effects begin to influencethe relationship between the measured structural response, i.e. thephase lag in the two legs of the meters and the natural frequency, andthe sought fluid parameters, i.e. the mass flow of the fluid and fluiddensity.

However, what is disclosed herein is to use a sound-speed based gasvolume fraction parameter, a reduced frequency parameter relating tophase lag to mass flow rate.

If the reduced frequency based on diameter is non-negligible, theinertial load from the fluid on the pipe develops a slight phase lagsthat increases with increasing frequency. For non-negligible reducedfrequencies based on the length of the flow tube, oscillations in theflow velocity can vary over the length of the pipe, potentiallyintroducing error in the output of the meter. Typical variations inmixture sound speeds due to two phase flow result in significantvariations in reduced frequencies.

Thus, by dramatically reducing mixture speed of sound, the introductionof gas to a liquid mixture can dramatically increase the reducedfrequency of the primary vibration associated with the Coriolis meter.If not accounted for in the interpretation, this increase in reducedfrequency renders the quasi-steady model increasing inaccurate, andresults in errors in mass flow and in density.

This decrease in accuracy of Corilois meters with the introduction ofbubbly fluids is well documented. In fact, others have attempted tocorrect for the effect of entrained air by correlating observed errorsin mass flow to the gas volume fraction within the process fluid. Theseauthors proposed a correction based on GVF as follows:

$R = \frac{2\alpha}{1 - \alpha}$

Where the α represents the gas volume fraction and R represents decreasein measured (apparent) mass flow normalized by the true mass flow. Thus,using this correlation, a 1% increase in entrained air would result in aroughly 2% underestimate of the actual mass flow.

Although this formulation appears to capture the general trend observedexperimentally, it has two drawbacks for use in the field. Firstly, thecoriolis meter 16 has no direct way to measure the gas volume fraction.It has been suggested to use the measured apparent density of the fluidto estimate the level of entrained air, however, this is problematicsince both of the two fundamental measurements, phase difference andnatural frequency, are impacted by changes in the reduced frequency ofthe Coriolis vibration. Secondly, it is unlikely that the gas volumefraction is the only variable influencing the relationship betweenmeasured phase difference and mass flow and the measured naturalfrequency and density. Although gas volume fraction appears to correlateover at least some range of parameters, the physics of the problemsuggest that sound speed, via a reduced frequency effect, may have alsodirect influence on the interpretation as developed above.

What is proposed in this disclosure is to use a direct sound measurementfrom the process fluid to aid in the interpretation of the coriolismeter 16. In this interpretation, the reduced frequency parametersdeveloped herein is included in interpreting the relation between thephase difference in the vibrating tubes and the mass flow as well as adirect role in interpreting the natural frequency of the oscillatingflow tubes in terms of process fluid density. The sound speedmeasurement, combined with knowledge of process liquid and gascomponents as well as process temperature and pressure, enables a directmeasurement of entrained air as well. Thus, the reduced frequencyparameter and gas volume fraction can be used as inputs in theinterpretation of phase lag in terms of mass flow.

Due to the strong relationship between air content in liquids andmixture sound speed, the role of the reduced frequency parameter in theinterpretation of the fundamental measurement of the Coriolis meter willhave a more pronounce effect in bubbly flows. However, changes in soundspeed and hence reduced frequency of operation in various types ofliquids and other process mixtures have an effect on the interpretationand hence accuracy of Coriolis meter used in these applications as well.Consider, flow example, the performance of a Coriolis meter on twoliquids—water and oil. Assume that the fluids have different densitiesand sound speeds. The different fluid properties suggest that theCoriolis meters will be operating at different reduced frequencies. Thereduced frequency for the water will typically be ˜10%–30% lower thanthat for the oil application.

Recognizing that, while they are different, the reduced frequencies forboth applications are still “small”, the impact on accuracy may not besignificant. However, some degree of inaccuracy is introduced by notaccounting for the differences in the reduced frequency of operation ofthe Coriolis meter in this application.

In this facility, water is pumped from the bottom of a large separatorthrough a mag meter which measures the volumetric flow rate of thewater. The water then flows through a SONARtrac entrained air meter toverify that the water has negligible entrained air. Air is then injectedinto the water forming a two phase mixture. The amount of entrained airis then measured with a second SONARtrac meter. The two phase mixture,of known water and air composition then passes through a 3 inch, benttube Corilois meter. The outputs of all of the above mentioned meteringdevices where recorded along with water pressure and temperature. Usingthis information, the errors associated with the coriolis meteroperating in the aerated liquids can be determined and plotted as afunction of sound speed based parameters. In this example, Coriolismeter performance is characterized as a function of gas volume fraction.The errors were indeed significant. At 2% entrained air, the Coriolismeter is over reporting mass flow by 15% and under reporting mixturedensity by 2%. The actual density being reported by the meter, ifinterpreted as the density of the liquid phase in the meter would beroughly 4% in error.

For this example, the mass flow error is parameterized by the soundspeed-based gas volume fraction of entrained air. The parametricdependence of this is given by the equation shown on the plot.Mass Factor=0.0147gvf^3−0.0018gvf^2+0.0041gvf+1.0009

This correlation was then used to correct for the coriolis mass flow forthe presence of entrained air. The amount of entrained air injectedupstream of the Coriolis meter was varied in small increments such thatthe total entrained air levels ranged from 0 to 2%. The Coriolis meterregisters and significant errors in mass flow (up to 15%) due toentrained air and the gas volume fraction based correlation employedsuccessfully corrects the mass flow errors to within roughly 1% for thedemonstration.

A flow measuring system 82 embodying the present invention may be usedmonitor well heads. A basic configuration of a well metering system 84is shown schematically in FIG. 9. This approach addresses most well headflow conditions and utilizes a two phase separator 86 (e.g., gas/liquidcylindrical cyclone (GLCC) separator) to separate the production streamof a gas/oil/water mixture 12 into a mostly gas stream 88 and a mostlyliquid stream 89. While a GLCC is provide in the metering system 84, thepresent invention contemplates any device that separates the air andliquid components.

The mostly gas stream 88 is fed to a sonar-based flow meter 89 similaras flow meter 90 which will be described in greater detail herein after.The flow meter measures the flow rate of the gas and determines the gasvolume fraction of the gas fluid.

The mostly liquid stream 89 is fed into a sonar-based flow meter 90,similar to the meters 18 and 100 of FIGS. 1 and 2 respectively, whichmeasures mixture sound speed and possibly convective velocity todetermine the gas volume fraction and the volumetric flow rate,respectively, of the liquid/gas mixture 89. The flow meter 90 is similarto that described in U.S. patent application Ser. No. 10/875,857 filedJun. 24, 2004, U.S. patent application Ser. No. 10/766,440 and U.S.patent application Ser. No. 10/762,410, which are incorporated herein byreference. Following the flow meter 90, the flow 89 enters a coriolismeter 16. A processing unit 92 receives the output signals from the flowmeter 90 and coriolis meter 16 to provide the measured outputs shown inFIGS. 3 and 8.

The two processing options for measuring the aerated liquid mass flowand density are presented in FIG. 7. The first method assumes that theperformance of the coriolis for both mass flow and density can beaugmented using the methods described in U.S. patent application Ser.No. 10/892,886 and U.S. Provisional Patent Application No. 60/539,640,which are incorporated herein by reference. The second approach,described in FIG. 11, assumes that only the density measurement of thecoriolis meter is used for the mass flow and density of the aeratedliquid. In this second approach, the volumetric flow rate determined bythe flow meter 90 is combined with the corrected density to determinemass flow when aeration levels (e.g., gas volume fraction) exceed athreshold value. This approach takes advantage of the present inventionsability to determine a mass flow rate compensated for entrained gas andthe coroilis ability to accurately mass flow rate for flows 12 havinglow levels of aeration.

The second approach can be described as follows. To determine thedensity, the speed of sound (SOS) measurement provided by the flow meter90 and the pressure (P) measurement provided by a pressure sensor 98 (ormay be estimated) are used to calculate gas volume fraction and/orreduced frequency parameter of the coriolis meter operating on theaerated fluid. Next the mixture density is determined by correcting theoutput of the Coriolis-based density meter for the effects of aeration(as described in similar to that described in U.S. patent applicationSer. No. 10/892,886. Direct measurement of the mixture density alongwith knowledge of the gas volume fraction and the gas density enablesdetermination of liquid phase density, as described hereinbefore.

Mass flow is determined via one of two methods, depending on the gasvolume fraction measurement of the flow meter 90. As shown in FIG. 11,if the gas volume fraction measurement is below a predetermined or inputthreshold level, the mass flow reported by the Coriolis is used. If itis above a threshold, the mass flow is calculated by first determiningthe total mixture volumetric flow rate by the flow meter 90 and thenmultiplying this value by corrected mixture density as described above.

The combination of mixture sound speed and density enables a fulldescription of the three phase fractions, i.e. the oil, water, and gasvolumetric phase fraction, as described hereinbefore in accordance withpresent invention and shown in FIG. 10.

The mostly gas stream 88 is feed in a sonar-based flow meter 99 similarto that described hereinbefore and in U.S. patent application Ser. No.10/875,857 filed Jun. 24, 2004, U.S. patent application Ser. No.10/766,440 and U.S. patent application Ser. No. 10/762,410. The flowmeter 99 measures sound speed and volumetric flow rate of the gas stream88, and optionally an orifice plate may be used to measure the gasstream momentum. Combination of volumetric flow, sound speed andmomentum measurements enables a good measurement of gas rate and liquidrate. The oil/water cut of the liquid phase of the mostly gas mixturecan be assumed to be the same as the oil/water cut of the mostly liquidstream.

The result is a compact, versatile, economical three phase meteringsystem.

Tests were conducted on such a well metering system similar to thatdescribed in FIG. 9 to evaluate the performance of the flow meter 90used in combination with the set-up shown in FIG. 9. FIGS. 12–14illustrated data recorded from the coriolis meter 16 and the flow meter90 to determine various parameters of the process fluid (e.g.,oil/water/gas mixture). Specifically, FIG. 12 shows the densitycorrection of the coriolis meter 16. FIG. 13 shows the net oil and watercut of the process fluid. FIG. 14 shows a snapshot of the oil productionbeing pumped from ground.

As one will appreciate, the sonar-based entrained air meter 16 enablescoriolis meters to maintain single phase accuracy in presence ofentrained air.

FIG. 15 illustrates a gas volume fraction meter 100 of FIG. 2, asdescribed herein before. The GVF meter 100 includes a sensing device 116disposed on the pipe 14 and a processing unit 124. The sensing device116 comprises an array of strain-based sensors or pressure sensors118–121 for measuring the unsteady pressures produced by acoustic wavespropagating through the flow 12 to determine the speed of sound (SOS).The pressure signals P₁(t)–P_(N)(t) are provided to the processing unit124, which digitizes the pressure signals and computes the SOS and GVFparameters. A cable 113 electronically connects the sensing device 116to the processing unit 124. The analog pressure sensor signalsP₁(t)–P_(N)(t) are typically 4–20 mA current loop signals.

The array of pressure sensors 118–121 comprises an array of at least twopressure sensors 118, 119 spaced axially along the outer surface 122 ofthe pipe 14, having a process flow 112 propagating therein. The pressuresensors 118–121 may be clamped onto or generally removably mounted tothe pipe by any releasable fastener, such as bolts, screws and clamps.Alternatively, the sensors may be permanently attached to, ported in orintegral (e.g., embedded) with the pipe 14. The array of sensors of thesensing device 116 may include any number of pressure sensors 118–121greater than two sensors, such as three, four, eight, sixteen or Nnumber of sensors between two and twenty-four sensors. Generally, theaccuracy of the measurement improves as the number of sensors in thearray increases. The degree of accuracy provided by the greater numberof sensors is offset by the increase in complexity and time forcomputing the desired output parameter of the flow. Therefore, thenumber of sensors used is dependent at least on the degree of accuracydesired and the desire update rate of the output parameter provided bythe apparatus 100. The pressure sensors 118–119 measure the unsteadypressures produced by acoustic waves propagating through the flow, whichare indicative of the SOS propagating through the fluid flow 12 in thepipe. The output signals (P₁(t)–P_(N)(t)) of the pressure sensors118–121 are provided to a pre-amplifier unit 139 that amplifies thesignals generated by the pressure sensors 118–121. The processing unit124 processes the pressure measurement data P₁(t)–P_(N)(t) anddetermines the desired parameters and characteristics of the flow 12, asdescribed hereinbefore.

The apparatus 100 also contemplates providing one or more acousticsources 127 to enable the measurement of the speed of sound propagatingthrough the flow for instances of acoustically quiet flow. The acousticsource may be a device the taps or vibrates on the wall of the pipe, forexample. The acoustic sources may be disposed at the input end of outputend of the array of sensors 118–121, or at both ends as shown. Oneshould appreciate that in most instances the acoustics sources are notnecessary and the apparatus passively detects the acoustic ridgeprovided in the flow 12, as will be described in greater detailhereinafter. The passive noise includes noise generated by pumps,valves, motors, and the turbulent mixture itself.

As suggested and further described in greater detail hereinafter, theapparatus 10 has the ability to measure the speed of sound (SOS) bymeasuring unsteady pressures created by acoustical disturbancespropagating through the flow 12. Knowing or estimating the pressureand/or temperature of the flow and the speed of sound of the acousticdisturbances or waves, the processing unit 124 can determine gas volumefraction, such as that described in U.S. patent application Ser. No.10/349,716, filed Jan. 23, 2003, U.S. patent application Ser. No.10/376,427, filed Feb. 26, 2003, U.S. patent application Ser. No.10/762,410, filed Jan. 21, 2004, which are all incorporated byreference.

Similar to the apparatus 100 of FIG. 15, an apparatus 200 of FIG. 16embodying the present invention has an array of at least two pressuresensors 118,119, located at two locations x₁, x₂ axially along the pipe14 for sensing respective stochastic signals propagating between thesensors 118,119 within the pipe at their respective locations. Eachsensor 118,119 provides a signal indicating an unsteady pressure at thelocation of each sensor, at each instant in a series of samplinginstants. One will appreciate that the sensor array may include morethan two pressure sensors as depicted by pressure sensor 120,121 atlocation x₃, x_(N). The pressure generated by the acoustic pressuredisturbances may be measured through strained-based sensors and/orpressure sensors 118–121. The pressure sensors 118–121 provide analogpressure time-varying signals P₁(t),P₂(t),P₃(t),P_(N)(t) to the signalprocessing unit 124. The processing unit 124 processes the pressuresignals to first provide output signals 151,155 indicative of the speedof sound propagating through the flow 12, and subsequently, provide aGVF measurement in response to pressure disturbances generated byacoustic waves propagating through the flow 12.

The processing unit 124 receives the pressure signals from the array ofsensors 118–121. A data acquisition unit 154 digitizes pressure signalsP₁(t)–P_(N)(t) associated with the acoustic waves 14 propagating throughthe pipe 114. An FFT logic 156 calculates the Fourier transform of thedigitized time-based input signals P₁(t)–P_(N)(t) and provide complexfrequency domain (or frequency based) signals P₁(ω),P₂(ω),P₃(ω),P_(N)(ω)indicative of the frequency content of the input signals.

A data accumulator 158 accumulates the additional signals P₁(t)–P_(N)(t)from the sensors, and provides the data accumulated over a samplinginterval to an array processor 160, which performs a spatial-temporal(two-dimensional) transform of the sensor data, from the xt domain tothe k-ω domain, and then calculates the power in the k-ω plane, asrepresented by a k-ω plot, similar to that provided by the convectivearray processor 146.

To calculate the power in the k-ω plane, as represented by a k-ω plot(see FIG. 17) of either the signals or the differenced signals, thearray processor 160 determines the wavelength and so the (spatial)wavenumber k, and also the (temporal) frequency and so the angularfrequency ω, of various of the spectral components of the stochasticparameter. There are numerous algorithms available in the public domainto perform the spatial/temporal decomposition of arrays of sensor units118–121.

In the case of suitable acoustic waves being present in both axialdirections, the power in the k-ω plane shown in a k-ω plot of FIG. 17 sodetermined will exhibit a structure that is called an acoustic ridge170,172 in both the left and right planes of the plot, wherein one ofthe acoustic ridges 170 is indicative of the speed of sound traveling inone axial direction and the other acoustic ridge 172 being indicative ofthe speed of sound traveling in the other axial direction. The acousticridges represent the concentration of a stochastic parameter thatpropagates through the flow and is a mathematical manifestation of therelationship between the spatial variations and temporal variationsdescribed above. Such a plot will indicate a tendency for k-ω pairs toappear more or less along a line 170,172 with some slope, the slopeindicating the speed of sound.

The power in the k-ω plane so determined is then provided to an acousticridge identifier 162, which uses one or another feature extractionmethod to determine the location and orientation (slope) of any acousticridge present in the left and right k-ω plane. The velocity may bedetermined by using the slope of one of the two acoustic ridges 170,172or averaging the slopes of the acoustic ridges 170,172.

Finally, information including the acoustic ridge orientation (slope) isused by an analyzer 164 to determine the flow parameters relating tomeasured speed of sound, such as the consistency or composition of theflow, the density of the flow, the average size of particles in theflow, the air/mass ratio of the flow, gas volume fraction of the flow,the speed of sound propagating through the flow, and/or the percentageof entrained air within the flow.

An array processor 160 uses standard so-called beam forming, arrayprocessing, or adaptive array-processing algorithms, i.e. algorithms forprocessing the sensor signals using various delays and weighting tocreate suitable phase relationships between the signals provided by thedifferent sensors, thereby creating phased antenna array functionality.In other words, the beam forming or array processing algorithmstransform the time domain signals from the sensor array into theirspatial and temporal frequency components, i.e. into a set of wavenumbers given by k=2π/λ where λ is the wavelength of a spectralcomponent, and corresponding angular frequencies given by ω=2πν.

One such technique of determining the speed of sound propagating throughthe flow 12 is using array processing techniques to define an acousticridge in the k-ω plane as shown in FIG. 17. The slope of the acousticridge is indicative of the speed of sound propagating through the flow12. The speed of sound (SOS) is determined by applying sonar arrayingprocessing techniques to determine the speed at which the onedimensional acoustic waves propagate past the axial array of unsteadypressure measurements distributed along the pipe 14.

The apparatus 200 of the present invention measures the speed of sound(SOS) of one-dimensional sound waves propagating through the mixture todetermine the gas volume fraction of the mixture. It is known that soundpropagates through various mediums at various speeds in such fields asSONAR and RADAR fields. The speed of sound propagating through the pipeand flow 12 may be determined using a number of known techniques, suchas those set forth in U.S. patent application Ser. No. 09/344,094, filedJun. 25, 1999, now U.S. Pat. No. 6,354,147; U.S. patent application Ser.No. 10/795,111, filed Mar. 4, 2004; U.S. patent application Ser. No.09/997,221, filed Nov. 28, 2001, now U.S. Pat. No. 6,587,798; U.S.patent application Ser. No. 10/007,749, filed Nov. 7, 2001, and U.S.patent application Ser. No. 10/762,410, filed Jan. 21, 2004, each ofwhich are incorporated herein by reference.

While the sonar-based flow meter using an array of sensors 118–121 tomeasure the speed of sound of an acoustic wave propagating through themixture is shown and described, one will appreciate that any means formeasuring the speed of sound of the acoustic wave may used to determinethe entrained gas volume fraction of the mixture/fluid or othercharacteristics of the flow described hereinbefore.

The analyzer 164 of the processing unit 124 provides output signalsindicative of characteristics of the process flow 12 that are related tothe measured speed of sound (SOS) propagating through the flow 12. Forexample, to determine the gas volume fraction (or phase fraction), theanalyzer 164 assumes a nearly isothermal condition for the flow 12. Assuch the gas volume fraction or the void fraction is related to thespeed of sound by the following quadratic equation:Ax ² +Bx+C=0

wherein x is the speed of sound, A=1+rg/rl*(K_(eff)/P−1)−K_(eff)/P,B=K_(eff)/P−2+rg/rl; C=1−K_(eff)/rl*a_(meas^)2); Rg=gas density,rl=liquid density, K_(eff)=effective K (modulus of the liquid andpipewall), P=pressure, and a_(meas)=measured speed of sound.

Effectively,

Gas Voulume Fraction (GVF)=(−B+sqrt(B^2−4*A*C))/(2*A)

Alternatively, the sound speed of a mixture can be related to volumetricphase fraction (φ_(i)) of the components and the sound speed (a) anddensities (ρ) of the component through the Wood equation.

$\frac{1}{\rho_{mix}a_{{mix}_{\infty}}^{2}} = {{\sum\limits_{i = 1}^{N}{\frac{\phi_{i}}{\rho_{i}a_{i}^{2}}\mspace{20mu}{where}\mspace{20mu}\rho_{mix}}} = {\sum\limits_{i = 1}^{N}{\rho_{i}\phi_{i}}}}$

One dimensional compression waves propagating within a flow 12 containedwithin a pipe 14 exert an unsteady internal pressure loading on thepipe. The degree to which the pipe displaces as a result of the unsteadypressure loading influences the speed of propagation of the compressionwave. The relationship among the infinite domain speed of sound anddensity of a mixture; the elastic modulus (E), thickness (t), and radius(R) of a vacuum-backed cylindrical conduit; and the effectivepropagation velocity (a_(eff)) for one dimensional compression is givenby the following expression:

$\begin{matrix}{a_{eff} = \frac{1}{\sqrt{{1/a_{{mix}_{\infty}}^{2}} + {\rho_{mix}\frac{2R}{Et}}}}} & \left( {{eq}\mspace{14mu} 1} \right)\end{matrix}$

The mixing rule essentially states that the compressibility of a mixture(1/(ρa²)) is the volumetrically-weighted average of thecompressibilities of the components. For gas/liquid mixtures 12 atpressure and temperatures typical of paper and pulp industry, thecompressibility of gas phase is orders of magnitudes greater than thatof the liquid. Thus, the compressibility of the gas phase and thedensity of the liquid phase primarily determine mixture sound speed, andas such, it is necessary to have a good estimate of process pressure tointerpret mixture sound speed in terms of volumetric fraction ofentrained gas. The effect of process pressure on the relationshipbetween sound speed and entrained air volume fraction is shown in FIG.18.

Some or all of the functions within the processing unit 24 may beimplemented in software (using a microprocessor or computer) and/orfirmware, or may be implemented using analog and/or digital hardware,having sufficient memory, interfaces, and capacity to perform thefunctions described herein.

While the embodiments of the present invention shown in FIGS. 2, 20 and21 shown the pressure sensors 118–121 disposed on the pipe 14, separatefrom the coriolis meter, the present invention contemplates that the GVFmeter 100 may be integrated with the coriolis meter to thereby provide asingle apparatus. In this integrated embodiment, the pressure sensors118–121 may be disposed on one or both of the tubes of the coriolismeter.

As shown in FIG. 19, the flow meter 100 may process the array ofpressure signals to determine the velocity and/or the volumetric flow offluid flow 12. The flow meter 100 embodying the present invention has anarray of at least two pressure sensors 118,119, located at two locationsx₁,x₂ axially along the pipe 14 for sensing respective stochasticsignals propagating between the sensors 118,119 within the pipe at theirrespective locations. Each sensor 118,119 provides a signal indicatingan unsteady pressure at the location of each sensor, at each instant ina series of sampling instants. One will appreciate that the sensor arraymay include more than two pressure sensors as depicted by pressuresensor 120,121 at location x₃, x_(N). The pressure generated by theconvective pressure disturbances (e.g., eddies 88, see FIG. 20) may bemeasured through strained-based sensors and/or pressure sensors 118–121.The pressure sensors 118–121 provide analog pressure time-varyingsignals P₁(t),P₂(t),P₃(t),P_(N)(t) to the signal processing unit 124.The processing unit 24 processes the pressure signals to first provideoutput signals indicative of the pressure disturbances that convect withthe flow 12, and subsequently, provide output signals in response topressure disturbances generated by convective waves propagating throughthe flow 12, such as velocity, Mach number and volumetric flow rate ofthe process flow 12.

The processing unit 24 receives the pressure signals from the array ofsensors 118–121. A data acquisition unit 140 (e.g., A/D converter)converts the analog signals to respective digital signals. The FFT logiccalculates the Fourier transform of the digitized time-based inputsignals P₁(t)–P_(N)(t) and provides complex frequency domain (orfrequency based) signals P₁(ω),P₂(ω),P₃(ω),P_(N)(ω) indicative of thefrequency content of the input signals. Instead of FFT's, any othertechnique for obtaining the frequency domain characteristics of thesignals P₁(t)–P_(N)(t), may be used. For example, the cross-spectraldensity and the power spectral density may be used to form a frequencydomain transfer functions (or frequency response or ratios) discussedhereinafter.

One technique of determining the convection velocity of the turbulenteddies 88 within the process flow 12 is by characterizing a convectiveridge of the resulting unsteady pressures using an array of sensors orother beam forming techniques, similar to that described in U.S. patentapplication Ser. No. 10/007,736 and U.S. patent application 6,889,562,Ser. No. 09/729,994, filed Dec. 4, 200, now U.S. Pat. No. 6,609,069,which are incorporated herein by reference.

A data accumulator 144 accumulates the frequency signals P₁(ω)–P_(N)(ω)over a sampling interval, and provides the data to an array processor146, which performs a spatial-temporal (two-dimensional) transform ofthe sensor data, from the xt domain to the k-ω domain, and thencalculates the power in the k-ω plane, as represented by a k-ω plot.

The array processor 146 uses standard so-called beam forming, arrayprocessing, or adaptive array-processing algorithms, i.e. algorithms forprocessing the sensor signals using various delays and weighting tocreate suitable phase relationships between the signals provided by thedifferent sensors, thereby creating phased antenna array functionality.In other words, the beam forming or array processing algorithmstransform the time domain signals from the sensor array into theirspatial and temporal frequency components, i.e. into a set of wavenumbers given by k=2π/λ where λ is the wavelength of a spectralcomponent, and corresponding angular frequencies given by ω=2πν.

The prior art teaches many algorithms of use in spatially and temporallydecomposing a signal from a phased array of sensors, and the presentinvention is not restricted to any particular algorithm. One particularadaptive array processing algorithm is the Capon method/algorithm. Whilethe Capon method is described as one method, the present inventioncontemplates the use of other adaptive array processing algorithms, suchas MUSIC algorithm. The present invention recognizes that suchtechniques can be used to determine flow rate, i.e. that the signalscaused by a stochastic parameter convecting with a flow are timestationary and have a coherence length long enough that it is practicalto locate sensor units apart from each other and yet still be within thecoherence length.

Convective characteristics or parameters have a dispersion relationshipthat can be approximated by the straight-line equation,k=ω/u,

where u is the convection velocity (flow velocity). A plot of k-ω pairsobtained from a spectral analysis of sensor samples associated withconvective parameters portrayed so that the energy of the disturbancespectrally corresponding to pairings that might be described as asubstantially straight ridge, a ridge that in turbulent boundary layertheory is called a convective ridge. What is being sensed are notdiscrete events of turbulent eddies, but rather a continuum of possiblyoverlapping events forming a temporally stationary, essentially whiteprocess over the frequency range of interest. In other words, theconvective eddies 88 is distributed over a range of length scales andhence temporal frequencies.

To calculate the power in the k-ω plane, as represented by a k-ω plot(see FIG. 21) of either the signals, the array processor 146 determinesthe wavelength and so the (spatial) wavenumber k, and also the(temporal) frequency and so the angular frequency ω, of various of thespectral components of the stochastic parameter. There are numerousalgorithms available in the public domain to perform thespatial/temporal decomposition of arrays of sensor units 118–121.

The present invention may use temporal and spatial filtering toprecondition the signals to effectively filter out the common modecharacteristics P_(common mode) and other long wavelength (compared tothe sensor spacing) characteristics in the pipe 14 by differencingadjacent sensors and retain a substantial portion of the stochasticparameter associated with the flow field and any other short wavelength(compared to the sensor spacing) low frequency stochastic parameters.

In the case of suitable turbulent eddies 88 (see FIG. 20) being present,the power in the k-ω plane shown in a k-ω plot of FIG. 21 shows aconvective ridge 200. The convective ridge represents the concentrationof a stochastic parameter that convects with the flow and is amathematical manifestation of the relationship between the spatialvariations and temporal variations described above. Such a plot willindicate a tendency for k-ω pairs to appear more or less along a line200 with some slope, the slope indicating the flow velocity.

Once the power in the k-ω plane is determined, a convective ridgeidentifier 148 uses one or another feature extraction method todetermine the location and orientation (slope) of any convective ridge200 present in the k-ω plane. In one embodiment, a so-called slantstacking method is used, a method in which the accumulated frequency ofk-ω pairs in the k-ω plot along different rays emanating from the originare compared, each different ray being associated with a different trialconvection velocity (in that the slope of a ray is assumed to be theflow velocity or correlated to the flow velocity in a known way). Theconvective ridge identifier 148 provides information about the differenttrial convection velocities, information referred to generally asconvective ridge information.

The analyzer 150 examines the convective ridge information including theconvective ridge orientation (slope). Assuming the straight-linedispersion relation given by k=ω/u, the analyzer 150 determines the flowvelocity, Mach number and/or volumetric flow. The volumetric flow isdetermined by multiplying the cross-sectional area of the inside of thepipe with the velocity of the process flow.

For any embodiments described herein, the pressure sensors, includingelectrical strain gages, optical fibers and/or gratings among others asdescribed herein, may be attached to the pipe by adhesive, glue, epoxy,tape or other suitable attachment means to ensure suitable contactbetween the sensor and the pipe. The sensors may alternatively beremovable or permanently attached via known mechanical techniques suchas mechanical fastener, spring loaded, clamped, clam shell arrangement,strapping or other equivalents. Alternatively, the strain gages,including optical fibers and/or gratings, may be embedded in a compositepipe. If desired, for certain applications, the gratings may be detachedfrom (or strain or acoustically isolated from) the pipe if desired.

It is also within the scope of the present invention that any otherstrain sensing technique may be used to measure the variations in strainin the pipe, such as highly sensitive piezoelectric, electronic orelectric, strain gages attached to or embedded in the pipe.Accelerometers may be also used to measure the unsteady pressures. Also,other pressure sensors may be used, as described in a number of theaforementioned patents, which are incorporated herein by reference.

In another embodiment, the sensor may comprise of piezofilm or strips(e.g. PVDF) as described in at least one of the aforementioned patentapplications.

While the illustrations show four sensors mounted or integrated in atube of the coriolis meter, the invention contemplates any number ofsensors in the array as taught in at least one of the aforementionedpatent applications. Also the invention contemplates that the array ofsensors may be mounted or integrated with a tube of a coriolis meterhaving shape, such as pretzel shape, U-shaped (as shown), straight tubeand any curved shape.

The invention further contemplated providing an elongated, non-vibrating(or oscillating) portion that permits a greater number of sensors to beused in the array.

While the present invention describes an array of sensors for measuringthe speed of sound propagating through the flow for use in interpretingthe relationship between coriolis forces and the mass flow through acoriolis meter. Several other methods exists.

For example, for a limited range of fluids, an ultrasonic device couldbe used to determine speed of sound of the fluid entering. It should benoted that the theory indicates that the interpretation of coriolismeters will be improved for all fluids if the sound speed of the processfluid is measured and used in the interpretation. Thus, knowing that thesound speed of the fluid is 5000 ft/sec as it would be for a water likesubstance, compared to 1500 ft/sec as it would be for say supercriticalethylene, would improve the performance of a coriolis based flow anddensity measurement. These measurements could be performed practicallyusing existing ultrasonic meters.

Another approach to determine speed of sound of the fluids is to measurethe resonant frequency of the acoustic modes of the flow tubes. Wheninstalled in a flow line, the cross sectional area changes associatedwith the transition from the pipe into the typically much smaller flowtubes creates a significant change in acoustic impedance. As a result ofthis change in impedance, the flow tube act as somewhat of a resonantcavity. By tracking the resonant frequency of this cavity, one coulddetermine the speed of sound of the fluid occupying the cavity. Thiscould be performed with a single pressure sensitive device, mountedeither on the coriolis meter, of on the piping network attached to thecoriolis meter.

In a more general aspect, the present invention contemplates the abilityto augmenting the performance of a coriolis meter using any method ormeans for measuring the gas volume fraction of the fluid flow.

In one embodiment of the present invention as shown in FIG. 20, each ofthe pressure sensors 118–121 may include a piezoelectric film sensor tomeasure the unsteady pressures of the fluid flow 12 using eithertechnique described hereinbefore.

The piezoelectric film sensors include a piezoelectric material or filmto generate an electrical signal proportional to the degree that thematerial is mechanically deformed or stressed. The piezoelectric sensingelement is typically conformed to allow complete or nearly completecircumferential measurement of induced strain to provide acircumferential-averaged pressure signal. The sensors can be formed fromPVDF films, co-polymer films, or flexible PZT sensors, similar to thatdescribed in “Piezo Film Sensors Technical Manual” provided byMeasurement Specialties, Inc., which is incorporated herein byreference. A piezoelectric film sensor that may be used for the presentinvention is part number 1-1002405-0, LDT4-028K, manufactured byMeasurement Specialties, Inc.

Piezoelectric film (“piezofilm”), like piezoelectric material, is adynamic material that develops an electrical charge proportional to achange in mechanical stress. Consequently, the piezoelectric materialmeasures the strain induced within the pipe 14 due to unsteady pressurevariations (e.g., acoustic waves) within the process mixture 12. Strainwithin the pipe is transduced to an output voltage or current by theattached piezoelectric sensor. The piezoelectrical material or film maybe formed of a polymer, such as polarized fluoropolymer, polyvinylidenefluoride (PVDF). The piezoelectric film sensors are similar to thatdescribed in U.S. patent application Ser. No. 10/712,818, U.S. patentapplication Ser. No. 10/712,833, and U.S. patent application Ser. No.10/795,111, which are incorporated herein by reference.

Another embodiment of the present invention include a pressure sensorsuch as pipe strain sensors, accelerometers, velocity sensors ordisplacement sensors, discussed hereinafter, that are mounted onto astrap to enable the pressure sensor to be clamped onto the pipe. Thesensors may be removable or permanently attached via known mechanicaltechniques such as mechanical fastener, spring loaded, clamped, clamshell arrangement, strapping or other equivalents. These certain typesof pressure sensors, it may be desirable for the pipe 12 to exhibit acertain amount of pipe compliance.

Instead of single point pressure sensors 118–121, at the axial locationsalong the pipe 12, two or more pressure sensors may be used around thecircumference of the pipe 12 at each of the axial locations. The signalsfrom the pressure sensors around the circumference at a given axiallocation may be averaged to provide a cross-sectional (or circumference)averaged unsteady acoustic pressure measurement. Other numbers ofacoustic pressure sensors and annular spacing may be used. Averagingmultiple annular pressure sensors reduces noises from disturbances andpipe vibrations and other sources of noise not related to theone-dimensional acoustic pressure waves in the pipe 12, thereby creatinga spatial array of pressure sensors to help characterize theone-dimensional sound field within the pipe 12.

The pressure sensors 118–121 of FIG. 20 described herein may be any typeof pressure sensor, capable of measuring the unsteady (or ac or dynamic) pressures within a pipe 14, such as piezoelectric, optical,capacitive, resistive (e.g., Wheatstone bridge), accelerometers (orgeophones), velocity measuring devices, displacement measuring devices,etc. If optical pressure sensors are used, the sensors 118–121 may beBragg grating based pressure sensors, such as that described in U.S.patent application, Ser. No. 08/925,598, entitled “High SensitivityFiber Optic Pressure Sensor For Use In Harsh Environments”, filed Sep.8, 1997, now U.S. Pat. No. 6,016,702, and in U.S. patent application,Ser. No. 10/224,821, entitled “Non-Intrusive Fiber Optic Pressure Sensorfor Measuring Unsteady Pressures within a Pipe”, which are incorporatedherein by reference. In an embodiment of the present invention thatutilizes fiber optics as the pressure sensors 14 they may be connectedindividually or may be multiplexed along one or more optical fibersusing wavelength division multiplexing (WDM), time division multiplexing(TDM), or any other optical multiplexing techniques.

In certain embodiments of the present invention, a piezo-electronicpressure transducer may be used as one or more of the pressure sensors115–118 and it may measure the unsteady (or dynamic or ac) pressurevariations inside the pipe or tube 14 by measuring the pressure levelsinside of the tube. These sensors may be ported within the pipe to makedirect contact with the mixture 12. In an embodiment of the presentinvention, the sensors 14 comprise pressure sensors manufactured by PCBPiezotronics. In one pressure sensor there are integrated circuitpiezoelectric voltage mode-type sensors that feature built-inmicroelectronic amplifiers, and convert the high-impedance charge into alow-impedance voltage output. Specifically, a Model 106B manufactured byPCB Piezotronics is used which is a high sensitivity, accelerationcompensated integrated circuit piezoelectric quartz pressure sensorsuitable for measuring low pressure acoustic phenomena in hydraulic andpneumatic systems. It has the unique capability to measure smallpressure changes of less than 0.001 psi under high static conditions.The 106B has a 300 mV/psi sensitivity and a resolution of 91 dB (0.0001psi).

The pressure sensors incorporate a built-in MOSFET microelectronicamplifier to convert the high-impedance charge output into alow-impedance voltage signal. The sensor is powered from aconstant-current source and can operate over long coaxial or ribboncable without signal degradation. The low-impedance voltage signal isnot affected by triboelectric cable noise or insulationresistance-degrading contaminants. Power to operate integrated circuitpiezoelectric sensors generally takes the form of a low-cost, 24 to 27VDC, 2 to 20 mA constant-current supply. A data acquisition system ofthe present invention may incorporate constant-current power fordirectly powering integrated circuit piezoelectric sensors.

Most piezoelectric pressure sensors are constructed with eithercompression mode quartz crystals preloaded in a rigid housing, orunconstrained tourmaline crystals. These designs give the sensorsmicrosecond response times and resonant frequencies in the hundreds ofkHz, with minimal overshoot or ringing. Small diaphragm diameters ensurespatial resolution of narrow shock waves.

The output characteristic of piezoelectric pressure sensor systems isthat of an AC-coupled system, where repetitive signals decay until thereis an equal area above and below the original base line. As magnitudelevels of the monitored event fluctuate, the output remains stabilizedaround the base line with the positive and negative areas of the curveremaining equal.

It is also within the scope of the present invention that any strainsensing technique may be used to measure the variations in strain in thepipe, such as highly sensitive piezoelectric, electronic or electric,strain gages and piezo-resistive strain gages attached to the pipe 12.Other strain gages include resistive foil type gages having a race trackconfiguration similar to that disclosed U.S. patent application Ser. No.09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147, which isincorporated herein by reference. The invention also contemplates straingages being disposed about a predetermined portion of the circumferenceof pipe 12. The axial placement of and separation distance ΔX₁, ΔX₂between the strain sensors are determined as described herein above.

It is also within the scope of the present invention that any otherstrain sensing technique may be used to measure the variations in strainin the tube, such as highly sensitive piezoelectric, electronic orelectric, strain gages attached to or embedded in the tube 14.

While a number of sensor have been described, one will appreciate thatany sensor the measures the speed of sound propagating through the fluidmay be used with the present invention, including ultrasonic sensors.

The coriolis meter described herein before may be any known coriolismeter, such as two inch bent tube coriolis meter manufactured myMicroMotion Inc. and a two in straight tube coriolic meter manufacturedby Endress & Hauser Inc. The coriolis meters comprise a pair of benttubes (e.g. U-shaped, pretzel shaped) or straight tubes.

While a particular density meter was described for an embodiment, thepresent invention contemplates any density meter may be used in theembodiments. Similarly, while a particular meter was provided todetermine speed of sound propagating through the fluid flow 12, thepresent invention contemplates any SOS measuring device may be used.

The dimensions and/or geometries for any of the embodiments describedherein are merely for illustrative purposes and, as such, any otherdimensions and/or geometries may be used if desired, depending on theapplication, size, performance, manufacturing requirements, or otherfactors, in view of the teachings herein.

It should be understood that, unless stated otherwise herein, any of thefeatures, characteristics, alternatives or modifications describedregarding a particular embodiment herein may also be applied, used, orincorporated with any other embodiment described herein. Also, thedrawings herein are not drawn to scale.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

1. A flow measuring system for determining the density of an aerated fluid flowing in a pipe, the flow measuring system comprising: a density meter that provides a density signal indicative of the density of the fluid flowing in the pipe; a flow measuring device including at least one sensor that measures the speed of sound propagating through the fluid, the flow measuring device providing an SOS signal indicative of the speed of sound propagating through the fluid and/or a GVF signal indicative of the gas volume fraction of the fluid; and a processing unit that determines the density of the non-gaseous component of the aerated fluid in response to the SOS signal and/or the GVF signal and the density signal.
 2. The flow measuring system of claim 1, wherein the speed of sound measurement is used to determine a gas volumetric fraction (GVF) in the flow of the fluid.
 3. The flow measuring system of claim 1, wherein the density meter includes one of a nuclear densitometer, a vibrating vane densitometer and a coriolis meter.
 4. The flow measuring system of claim 1, wherein the at least one sensor includes at least two pressure strain sensors at different axial locations along the pipe, each of the pressure strain sensors providing a respective pressure strain signal indicative of an acoustic pressure disturbance within the pipe at a corresponding axial position.
 5. The flow measuring system of claim 1, wherein the at least one sensor includes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16 strain based sensors disposed axially along the pipe.
 6. The flow measuring system of claim 1, wherein the gas volume fraction is determined using the following formula: Gas Voulume Fraction=−B+sqrt(B^2−4*A*C))/(2*A) wherein A=1rg/rl*(K_(eff)/P−1)−K_(eff)/P, B=K_(eff)/P−2+rg/rl; C=1−K_(eff)/rl*a_(meas)^2; Rg=gas density, rl=liquid density, K_(eff) effective K (modulus of the liquid and pipewall), P=pressure, and a_(meas)=measured speed of sound.
 7. The flow measuring system of claim 1, wherein the processing unit determines a slope of an acoustic ridge in the k-ω plane, in response to the pressure signals, to provide a SOS signal indicative of the speed of sound propagating through the fluid.
 8. The flow measuring system of claim 1, wherein the density of the non-gaseous components of the fluid is determined using the following equation: ρ_(nongas)=ρ_(mix)/(1−φ_(gas)) wherein ρ_(mix) is the density of the mixture, ρ_(nongas), ø_(nongas) are the density and phase fraction, respectively, of a non-gas component of the fluid flow, and ρ_(gas), ø_(gas) are the density and phase fraction, respectively, of the entrained gas within the mixture.
 9. The flow measuring system of claim 1, wherein the speed of sound is associated with acoustic waves that are one dimensional acoustic waves propagating axially through the pipe.
 10. The flow measuring system of claim 9, wherein the acoustic waves are passive noise.
 11. The flow measuring system of claim 1, wherein the processor provides a signal indicative of the volumetric phase fraction of the non-gaseous components of the fluid, wherein the non-gaseous components comprise two components.
 12. The flow measuring system of claim 11, wherein the non-gaseous components of the fluid consist of liquid/liquid components or liquid/solid components of the fluid.
 13. The flow measuring system of claim 11, wherein the volumetric phase fraction of each of the non-gaseous components of the fluid is determined solving the following equations: ρ_(mix)=ρ₁φ₁+ρ₂φ₂+ρ_(gas)φ_(gas); and φ_(gas)+φ₁+φ₂=1 wherein ρ_(mix) is the density of the mixture, ρ₁, ρ₂ are the density of two non-gaseous components of the fluid, and ø₁, ø₂ are the phase fraction of two non-gaseous components of the fluid, and ρ_(gas), ø_(gas) are the density and phase fraction, respectively, of the entrained gas within the fluid.
 14. The flow measuring system of claim 1, wherein the flow measuring device comprises an array of sensors disposed axially along the pipe for measuring acoustic pressures in the fluid, and providing respective pressure signals.
 15. The flow measuring system of claim 14, wherein the array of sensors includes at least one of strain based sensors, pressure sensors, ported pressure sensors and ultra-sonic sensors.
 16. A method for determining the density of an aerated fluid flowing in a pipe, the method comprising: providing a density signal indicative of the density of the fluid flowing in the pipe; providing an SOS signal indicative of the speed of sound propagating through the fluid and/or a GVF signal indicative of the gas volume fraction of the fluid; and determining the density of the non-gaseous component of the aerated fluid in response to the SOS signal and/or the GVF signal and the density signal.
 17. The method of claim 16, further includes determining the GVF signal in response to the SOS signal.
 18. The method of claim 16, further includes determining the GVF signal using the following formula: Gas Voulume Fraction=−B+sqrt(B^2−4*A*C))/(2*A) wherein A=1rg/rl*(K_(eff)/P−1)−K_(eff)/P, B=K_(eff)/P−2+rg/rl; C=1−K_(eff)/rl*a_(meas)^2; Rg=gas density, rl=liquid density, K_(eff) effective K (modulus of the liquid and pipewall), P=pressure, and a_(meas)=measured speed of sound.
 19. The method of claim 16, wherein determining the density of the non-gaseous components of the fluid is determined using the following equation: ρ_(nongas)=ρ_(mix)/(1−φ_(gas)) wherein ρ_(mix) is the density of the mixture, ρ_(nongas), ø_(nongas) are the density and phase fraction, respectively, of a non-gas component of the fluid flow, and ρ_(gas), ø_(gas) are the density and phase fraction, respectively, of the entrained gas within the mixture.
 20. The method of claim 16, further includes measuring the density of the fluid to provide the density signal.
 21. The method of claim 16, wherein the speed of sound is associated with acoustic waves that are one dimensional acoustic waves propagating axially through the pipe.
 22. The method of claim 21, wherein the sound waves are passive noise.
 23. The method of claim 16, further includes providing a signal indicative of the volumetric phase fraction of the non-gaseous components of the fluid, wherein the non-gaseous components comprise two components.
 24. The method of claim 23, wherein the non-gaseous components of the fluid consist of liquid/liquid components or liquid/solid components of the fluid.
 25. The method of claim 23, wherein the volumetric phase fraction of each of the non-gaseous components of the fluid is determined salving the following equations: ρ_(mix)=ρ₁φ₁+ρ₂φ₂+ρ_(gas)φ_(gas); and φ_(gas)+φ₁+φ₂=1 wherein ρ_(mix) is the density of the mixture, ρ₁, ρ₂ are the density of two non-gaseous components of the fluid, and ø₁, ø₂ are the phase fraction of two non-gaseous components of the fluid, and ρ_(gas), ρ_(gas) are the density and phase fraction, respectively, of the entrained gas within the fluid.
 26. The method of claim 20, further includes using one of a nuclear densitometer, a vibrating vane densitometer and a coriolis meter to measure the density of the fluid.
 27. The method of claim 16, further includes measuring the speed of sound propagating through the fluid to provide the SOS signal indicative of the speed of sound propagating through the fluid and/or the GVF signal indicative of the gas volume fraction of the fluid.
 28. The method of claim 27, wherein measuring the speed of sound includes using an array of sensors disposed axially along the pipe for measuring acoustic pressures in the fluid and providing respective pressure signals.
 29. The method of claim 28, wherein determining the SOS signal and/or GVF signal includes determining a slope of an acoustic ridge in the k-ω plane, in response to the pressure signals, to provide a SOS signal indicative of the speed of sound propagating through the fluid.
 30. The method claim 28, wherein the array of sensors includes at least one of strain based sensors, pressure sensors, ported pressure sensors and ultra-sonic sensors.
 31. The method of claim 28, wherein the array of sensors includes at least two pressure strain sensors at different axial locations along the pipe, each of the pressure strain sensors providing a respective pressure strain signal indicative of an acoustic pressure disturbance within the pipe at a corresponding axial position.
 32. The method of claim 28, wherein the array of sensors includes 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16 strain based sensors disposed axially along the pipe. 